How do you factor $(3x-5)^3-125$ ?

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Answer 1 · 2016-07-18T12:20:24

$(3x-5)^3-125=(3x-10)(9x^2-15x+25)$

To factorize $(3x-5)^3-125$ , as it is difference of two cubes, we can use the identity $a^3-b^3=(a+b)(a^2+ab+b^2)$ . Hence,

$(3x-5)^3-125$

= $(3x-5-5)((3x-5)^2+5(3x-5)+5^2$

= $(3x-10)(9x^2-30x+25+15x-25+25)$

= $(3x-10)(9x^2-15x+25)$

How do you factor (3x-5)^3-125(3x-5)^3-125?